Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Journal of Physics

Ising Model on a checkerboard Lattice with Crossing Interactions

Ken‐Yu Lin

Published Aug 1, 1988• 0 citations
OpenAlex

Abstract

A formula for the spontaneous magnetization of the Ising model on a checkerboard lattice with crossing interactions is proposed. Our conjecture agrees with the exact low-temperature series expansion up to the 18th order.

Related papers

High-Temperature Series Expansions of Susceptibility of Ising Model on Checkerboard Lattice with Crossing Interactions

Jeng-Ming Chen, Keh-Ying Lin

Chinese Journal of Physics•Aug 1, 1996•0 citations

Spontaneous magnetisations of the Ising model on the bathroom tile lattice

R. J. Baxter, T. C. Choy

The authors evaluate the site spontaneous magnetisations on the general 4-8 or bathroom tile lattice using mappings to checkerboard, free-fermion and Union Jack Ising models. Their results verify the conjecture of Lin et al (1987), who proposed their formula from twelfth-order low-temperature series expansions.

Journal of Physics A Mathematical and General•May 7, 1988•15 citations

Magnetization of the three-spin triangular Ising model

R. J. Baxter, M F Sykes, M G Watts

Below its critical temperature, the triangular Ising model with pure three-spin interactions has a spontaneous magnetization M. The first 13 terms of a series expansion for M are known. Here these are re-arranged into a form which can be extrapolated to all terms in a natural way. Thus a conjecture is obtained for M. It fits the scaling prediction beta =1/12. Another order parameter is similarly discussed, together with the difficulties encountered in applying the technique to the two-spin Ising model susceptibility.

Journal of Physics A Mathematical and General•Feb 1, 1975•55 citations

Exact solution of the Ising model on a pentagonal lattice

Viktor Urumov

It is shown that the Ising model on a two-dimensional lattice with pentagonal tiling and nearest-neighbour interactions is equivalent to the Ising model on the Union-Jack lattice with nearest- and second nearest-neighbour non-crossing interactions. Besides the critical temperature, exact expressions are obtained for the spontaneous magnetization for both types of lattice sites.

Journal of Physics A Mathematical and General•Aug 13, 2002•23 citations

LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

Yee-Mou Kao, MALL CHEN, Keh Ying Lin

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

International Journal of Modern Physics B•Dec 20, 2002•0 citations

Low-temperature expansions for Ising models with four-spin interactions

J. Oitmaa

Low-temperature series for the spontaneous magnetization are derived for two Ising models with four-spin interactions-(i) a model studied previously by the author using high temperature series, (ii) a model equivalent to Baxter's (1973) eight-vertex model. In the former case the exponent beta appears to remain constant at 1/8, independent of J 4 , the strength of the four-spin interaction; for the eight-vertex model beta varies continuously with J 4 as expected.

Journal of Physics C Solid State Physics•Jan 21, 1974•14 citations
Below its critical temperature, the triangular Ising model with pure three-spin interactions has a spontaneous magnetization M. The first 13 terms of a series expansion for M are known. Here these are re-arranged into a form which can be extrapolated to all terms in a natural way. Thus a conjecture is obtained for M. It fits the scaling prediction beta =1/12. Another order parameter is similarly discussed, together with the difficulties encountered in applying the technique to the two-spin Ising model susceptibility.
We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.